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Course Overview

It has been called the third great revolution of 20th-century physics, after relativity and quantum theory. But how can something called chaos theory help you understand an orderly world? What practical things might it be good for? What, in fact, is chaos theory? "Chaos theory," according to Dr. Steven Strogatz, Director of the Center for Applied Mathematics at Cornell University, "is the science of how things change." It describes the behavior of any system whose state evolves over time and whose behavior is sensitive to small changes in its initial conditions.

The 24 lectures of Chaos take you to the heart of chaos theory as it is understood today. Taught by Professor Strogatz, an award-winning Ivy League professor and a scientist described by Nature magazine as "one of the most creative biomathematicians of the past few decades," Chaos introduces you to a fascinating discipline that has more to do with your everyday life than you may realize.

A Revolutionary Way of Thinking

Surprisingly, you have already encountered chaos theory before, although you might not have recognized it at the time. From the flapping of a butterfly's wings to the dripping of a leaky faucet, chaos theory draws a wealth of unordinary insight from the most ordinary of occurrences.

Chaos theory affects nearly every field of human knowledge and endeavor, from astronomy and zoology to the arts, the humanities, and business. It can:

help analysts understand price fluctuations in the stock market,

ensure a smooth flow of data traffic on the Internet, and

show insurance companies how to manage the risks of natural catastrophes.

This course shows you the importance of this revolutionary field and how it has helped us come closer than ever to solving some of life's mysteries. Today, the underlying mathematics of science's major unsolved problems—including the nature of consciousness, the origin of life, and cancer—are essentially nonlinear; express any of these problems as a mathematical system and you learn that the whole may be either more or less than the sum of its parts.

In its ability to tackle bewilderingly complex problems, chaos theory has revolutionized the way we perceive the world around us. It allows scientists to reach beyond a dependency on the analytical limitations of the deterministic, "clockwork" universe that was the legacy of thinkers like Galileo, Kepler, and especially Newton.

Throughout the lectures, Professor Strogatz makes the case for why chaos theory marks such a radical departure from traditional science:

It asks unusual questions at the everyday scale of human life.

It shifts the focus off the laws of nature and onto their consequences.

It uses the computer not as a calculating tool but as a means of amplifying intuition.

It does not reduce complex problems into their separate parts but puts the parts back together to help understand the whole.

It is radically interdisciplinary in an era of increasingly specialized disciplines.

It paints a topsy-turvy picture of the world in which simple systems can show complex behavior.

It is a scientific field in which change came about suddenly.

Follow the Exciting Story of Chaos

As you delve into this ever-evolving field, you learn the surprising tale of how chaos theory was discovered—a story that Professor Strogatz likens to a detective novel filled with twists and turns.

First glimpsed by the French mathematician Henri Poincaré, the notion of chaos theory was lost for nearly a century before being rediscovered—almost accidentally. It was revived by a mathematically oriented meteorologist named Edward Lorenz, whose development of the butterfly effect (the extreme sensitivity of a chaotic system to tiny changes in its initial conditions) had little impact until the 1970s and 1980s, when the wave of chaos theory finally crashed onto the shores of the scientific community.

As you follow the story of chaos theory's development, you approach the core ideas of chaos in the same way the world's greatest thinkers, grounded in their historical contexts, once did. This story not only helps you understand the fundamentals of this field, but it also helps you appreciate the extraordinary intellectual feat that chaos theory represents.

Learn Chaos Theory Visually

This course offers you a unique opportunity to get an expert's instruction on the field of chaos theory and is one of the only places outside the halls of academia where you can follow along with detailed computer graphics—specifically developed for this course—as visual aids.

A large portion of the course explores the intimate relationship between chaos theory and fractals: shapes or processes whose structures repeat ad infinitum such that the tiniest parts resemble the original whole. You see how fractals are unique from more commonly known shapes like circles and cubes and how they can be used to describe a variety of processes and phenomena like the jagged coastline of Norway or the drip paintings of Jackson Pollock.

Find the Unordinary in the Ordinary

Professor Strogatz's expert guidance lays bare the complexities of chaos theory in a way that any interested layperson can understand. With the insights he provides in Chaos, news stories about key scientific discoveries and new directions in research take on a fresh importance.

Professor Strogatz is a teacher repeatedly honored by institutions and students alike. During his tenure at the Massachusetts Institute of Technology, he received the E. M. Baker Memorial Award for Excellence in Undergraduate Teaching, the university's only institute-wide teaching prize selected and awarded solely by students. In 2007, he received a lifetime achievement award for the communication of mathematics to the general public from the Joint Policy Board for Mathematics, which represents the four major American mathematical societies.

Whether charting the exciting history of the field, focusing on fractals as "the footprints of chaos," or journeying to the frontiers of chaos research, this course shows you new ways to think about and view the world around you.

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24 lectures

| Average 30 minutes each

1

The Chaos Revolution

Chaos was once ignored by traditional science but is now both a pop sensation and a tremendously important field. But what is the science of chaos and why is it revolutionary and important? x

2

The Clockwork Universe

The scientific revolution launched by Galileo, Kepler, and Newton left a great legacy: the idea of an orderly universe ruled by mathematical laws. But is there something disquieting in the idea of a vast, impersonal, clockwork universe of determinism with no room for chance? x

3

From Clockwork to Chaos

By the late 19th century, three cracks appeared in determinism's foundations: relativity, quantum mechanics—and chaos. The "three-body problem" was considered the mathematical challenge of the era, and its solution, involving a still-unimagined chaos, eluded some of mathematics' greatest minds. x

4

Chaos Found and Lost Again

Henri Poincaré's groundbreaking work on the three-body problem implied that a system governed by deterministic laws could still be unpredictable; chaos had crept into the clockwork. Although Poincaré invented a new, visual way of thinking about the mathematics involved, his brilliant discovery was quickly forgotten. x

5

The Return of Chaos

For 70 years, chaos remained a scientific backwater. The calm ended with a thunderclap from a man fascinated by storms and weather. You see how Edward Lorenz discovered chaos in a model of weather patterns that allowed him to happen upon the "butterfly effect." x

6

Chaos as Disorder—The Butterfly Effect

The butterfly effect—the extreme sensitivity of a chaotic system to tiny changes in its initial conditions—has become part of popular culture but is frequently misunderstood. You begin to understand not only its importance and power but also its limitations. x

7

Picturing Chaos as Order—Strange Attractors

Your introduction to chaos has highlighted its unpredictable, random side, as exemplified by the butterfly effect. But there is also an amazing order inherent in chaos, and you learn how this can be visualized through the infinitely complex image known as a "strange attractor." x

8

Animating Chaos as Order—Iterated Maps

If a strange attractor is analogous to an image created through time-lapse photography, Lorenz's "iterated map" might be the product of a series of strobe-light photographs. But despite its profound implications, Lorenz's discovery failed to attract the scientific community's notice. x

9

How Systems Turn Chaotic

By the 1970s, there was an unprecedented convergence of disciplines. Researchers in mathematics, ecology, and fluid mechanics found themselves asking the same question: How does an orderly system suddenly turn chaotic? You see how a famous iterated map known as the logistic map reveals the most basic route. x

10

Displaying How Systems Turn Chaotic

You deepen your understanding of the logistic map with the icon of chaos known as the orbit diagram. Its breathtaking imagery amounts to a Rosetta Stone for making sense of certain forms of chaos in the natural world. x

11

Universal Features of the Route to Chaos

In 1978, physicist Mitchell Feigenbaum made a stunning breakthrough, showing that the logistic map displayed universal features so generic that they must also occur in nature, even though no laws of nature are built into it. You begin to understand how such universality arises. x

12

Experimental Tests of the New Theory

In the early 1980s, painstaking experiments on such disparate systems as swirling fluids, electronic circuits, and oscillating chemical reactions confirmed the predictions of chaos theory. Overreaching by some advocates, however, has provoked a backlash of skepticism to this day. x

13

Fractals—The Geometry of Chaos

The pioneers of chaos were bewildered by the fantastic shapes they encountered while trying to visualize chaos. In the first of several lectures devoted to these intricate shapes—now called fractals—you learn why they are so inextricably connected to chaos. x

14

The Properties of Fractals

You are introduced to the two most distinctive properties of fractals—inexhaustible structural richness and "self-similarity," or the resemblance of the parts to the whole—before learning how the science of fractals came into being and its situation in the broader scientific landscape. x

15

A New Concept of Dimension

Using some idealized geometric examples, you learn how to define the dimension of a fractal—discovering that the usual categories of one-, two-, or three-dimensional usually do not apply, and that fractals are so convoluted they fall somewhere in between, such as 1.26-dimensional! x

16

Fractals Around Us

Fractals are not merely static geometric shapes but also can represent erratic processes in time, such as fluctuating stock prices, Internet data bursts, or earthquakes. You learn that their gyrations are wilder and more frequent than conventional statistical methods would predict and make their management more complex. x

17

Fractals Inside Us

From lungs to nervous systems to the nutrient supply systems of plants, all living things are built from fractal networks. You examine this geometry of life, including a recent theory that invokes fractal architecture to explain one of the most comprehensive laws in biological science. x

18

Fractal Art

This lecture shows you some of the manifestations of fractals in art, including the controversial drip paintings of Jackson Pollock. Some have suggested that they contain fractal characteristics that changed over the course of his career in a very systematic way. x

19

Embracing Chaos—From Tao to Space Travel

Does chaos have practical applications? Because tiny nudges to a chaotic system can have potent effects, these systems are exceptionally responsive. You see the advantages of harnessing chaos in the dramatic story of how a NASA mathematician "surfed" the gravitational field to salvage a Japanese lunar mission gone wrong. x

20

Cloaking Messages with Chaos

Although the feasibility of encrypting electronic messages by cloaking them in chaotic "noise" has been verified in real-world tests, questions remain. Could an eavesdropper crack the chaos? This lecture shows you what such an application could mean in a world of growing concerns about cyberterrorism, national security, and cell phone and Internet privacy. x

21

Chaos in Health and Disease

Building on decades of biological research, chaos theorists have been asking questions about the dynamics of bodily rhythms. Can the mathematics of chaos help predict an epileptic seizure? Quell or prevent cardiac arrhythmias? Perhaps most controversially, can chaos in the body ever be a sign of health rather than of sickness? x

22

Quantum Chaos

Can chaos theory coexist with quantum theory? Can it survive the descent to the strange world of the atom, where Newtonian trajectories dissolve into a haze of quantum probability waves? You see how scientists reconcile two radically different views of reality. x

23

Synchronization

Large, complex systems having many interacting parts often display a remarkable capacity for organizing themselves, with their individual parts becoming synchronized. This lecture shows you systems as diverse as pendulum clocks, fireflies, heart cells, and menstrual cycles and takes you inside the opening-day swaying of London's Millennium Bridge. x

24

The Future of Science

You review what you've learned and examine the future role of chaos theory. In a world where most of the major unsolved issues facing science—including cancer, consciousness, the origin of life, and AIDS—involve fundamentally nonlinear systems, chaos theory can be a crucial first step toward their solution x

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Download 24 video lectures to your computer or mobile app

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24 lectures on 4 DVDs

152-page printed course guidebook

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Your professor

About Your Professor

Steven Strogatz, Ph.D.

Cornell University

Professor Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics and Professor of Theoretical and Applied Mechanics at Cornell University. He graduated summa cum laude from Princeton University with a B.A. in Mathematics and received his Ph.D. from Harvard University. Before joining Cornell University in 1994, Professor Strogatz was a faculty member at MIT. Professor Strogatz's books include Nonlinear...

Reviews

Chaos is rated
4.6 out of
5 by
102.

Rated 5 out of
5 by
Lawrence Long from
Very InterestingSince I am recovering from eye surgery and am supposed to avoiding reading, I am looking forward to go over the written version and probably watch the video which I mostly listened to the first time around.

Date published: 2019-06-06

Rated 5 out of
5 by
Brainiac from
very interesting subject. presentation clear, in depth, good balance between math
and general information. Strogratz very talented explainer.

Date published: 2019-05-30

Rated 5 out of
5 by
MarleysGhost from
The Tao of MathPrior to taking this course, I really knew nothing about Chaos Theory. Other than of course the casual references to things like “the butterfly effect” that appear in the popular press. I am ashamed that I was so ignorant that I pretty much equated chaos to randomness. Well, thanks to Professor Strogatz, no more. His approach to teaching the subject does not depend on the student’s knowledge of math (other than perhaps high school algebra) or physics but rather is inclusive enough that anyone interested can understand some of the concepts. No doubt this is due to very visual approach used in explaining many of the concepts. This is especially true of the many computer simulations presented that demonstrate points being made during the lectures.
In the beginning, I was a bit put off by Dr. Strogatz’s presentation style, but soon came to realize that it would be ideally suited in a small classroom setting and that all I had to do was watch and listen in that context. True enough some of his humor is a bit on the “geeky” side, but for me it was both charming and funny.
As Chaos Theory hit the big time well after my education, this course opened up a whole new way of considering many things that I had not considered in any depth or at all. I loved the references to philosophy and history. And to the continual inter-disciplinary direction that the field was taking. For example the discussion of the population growth of insects where we first seem some reasonably predictable (in a linear sense) increases that all of a sudden hit a threshold that at first seems to be complete randomness but is in fact not random at all (though chaotic) has a beauty that I needed to see to believe. Awesome! And then within the “windows” of the chaos, the periodicity of the patterns was unexpected, satisfying and surprising. Without much underlying mathematical explanation, Professor Strogatz manages to demonstrate from one simple, real-world example an underlying generalization of an unexpected way some of the world works.
Perhaps my only mild complaint is that the section on low-fuel space flights to the moon and elsewhere could have used a bit more detail, though perhaps doing so would not have fit within the low-math objective of the course. I am sure that the low-math approach is one required by TTC for many of its survey courses in science. Something hard to achieve and one where you hit the mark.

Date published: 2019-03-02

Rated 5 out of
5 by
Cheryl101 from
Very interesting topicIt is fun for me to learn about areas of science that have either come about after I left college, or just were not part of my curriculum. I was completely fascinated by this topic. I have heard references to this topic over the years, but never took the time to dig into it to see what all of the fuss was about.
I found the professor to be very passionate and enthusiastic about the topic which elevated my own interest level. Sometimes, professors are so polished in their presentations and simply stand behind a lectern and speak in nicely paced, eloquent manor. These are the types of lectures where the audio version works well for me. I am glad I got the video version for this course because the enthusiasm shows through and the graphics were very useful in understanding the content. I had no problems following content.
I had looked for other courses by this professor, but alas, did not find any. exept where the course is taught by multiple instructors.

Date published: 2018-09-12

Rated 5 out of
5 by
Curious Barb from
A most enjoyable course!A phrase running through this 72-year young head for some time, “There’s order in Chaos.” was satisfied. Dr. Strogatz’s enthusiasm, pacing and style of teaching were exceptional and frankly I was enthralled, as someone else said, I, too, was sitting on the edge of my seat and couldn’t wait for the next installment. The visual approach was particularly helpful as I am no mathematician. I thought the demonstrations, metaphors, ongoing reminders of concepts helped to ground the material. It is exciting to be introduced to the real life potential applications that can be achieved through non-linear problem-solving. I also took away the importance of interdisciplinary networking which will inform future directions in education and training. It’s all about systems. The course guidebook was very useful in it’s concise substantive summaries. I think the course requires curiosity and openness as well as willingness to concentrate and reflect. I would love to do another course with Dr. Strogatz.

Date published: 2018-07-31

Rated 5 out of
5 by
JoeLauzon from
great course contentI'm 77 years old but wish I was young enough to get professionally involved in this field; it looks so exciting!!

Date published: 2018-06-15

Rated 5 out of
5 by
ArthurS from
Essential for understanding extreme eventsI was totally enthralled by the coursework and discussion in Prof. Steven Strogatz's interesting and imaginative course. In fact, so taken was I with the subject that I immediately went out and bought one of the recommended readings that Prof. Strogatz includes in his list in his Course Guidebook. In this case, it was Benoit Mandelbrot's book on using fractional mathematical concepts as an aid to understanding financial markets and investments.
I am not a mathematician, nor have I been a member of any profession for which a working knowledge of advanced mathematics was either useful or required. However, the evidence and arguments marshaled by Prof. Strogatz about how fractals work in the real world (although not widely known until very recently) make a compelling case that this is essential knowledge for anyone who deals in matters involving statistics and probability. It is key to understanding the outsize impacts that randomness and volatility have on our lives and fortunes in ways that were unimaginable only a few years ago. Chaos Theory has gotten a lot of press in recent years, and these twenty-four lectures will have people sitting on the edge of their seats in rapt attention, learning why it is so important that these newly found knowledge be taught and understood, because we live in a world where instability and unpredictability abound, and which traditional mathematical models were completely inadequate to explain.

Date published: 2018-05-25

Rated 5 out of
5 by
M Rutkauskas from
Being with a genius teacherSuper course, a genius who knows how to teach. I think he could explain Maxwell's equations to me. Too bad he did only one course Chaos. I learned a lot from his asides, ideas I had heard bandied about for years in Scientific American but I never understood--2 body, 3 body problem, a little about calculus and its uses.
And I learned all about Chaos. I ordered two of the essential books he recommended, but could not wait and finished the course before I got them.
It's just wonderful and you can tell he enjoys teaching it. I checked out his college course on Chaos on youtube and he doesn't look anywhere near as happy! I think he especially enjoyed the opportunity to teach his favorite things to the 'public.' Where 'our' interests are more pure, and don't involve getting a grade.